Extend AC to E, make CE=BM, and connect DE (actually, rotate the triangle BDM to CDE).

In BDM and CDE triangle, it can be proved that

Angle MBD=DCE=90 degrees,

And BM=CE, BD=CD.

So the triangle BDM and CDE are congruent.

So DM=DE

In the triangle DMN and Deng

Proof angle MDN=EDN=60 degrees

And DM=DE, DN=DN.

So the triangle DMN and DEN are congruent.

So MN=NE=EC+CN=BM+CN.

2。 MN=CN-BM

Find point e on AC, make CE=BM, and then connect with DE.

Triangle BDM and CDE are congruent, triangle DMN and Deng Quan are congruent.

So MN=NE=CN-CE=CN-BM.